Combine logic gates to make a basic calculator?

I'm trying to learn how logic gates interact to create a calculator as we know it. Obviously in real scale, it's too small to observe, so I need some reference material. What I want to know is how I can take the binary equivalent of 2(which is 10), add 2 more, and get an output of the binary equivalent of 4(which is 100), only using logic gates? I understand the symbols, and such, I just don't understand how they combine. My plan is to simply draw it out, then simulate it on the computer, and finally implement in real life. Obviously, I won't be creating the most powerful super computer. But I'd like to just get a simple 8-bit ALU, that can add and subtract single digit numbers. I plan to keep it as simple as possible. Just using some loose wires as the binary input, and LEDs as the binary output. I can take care of the rest, like converting the LED signal into a 7-segment display, and such. But I need some reference material, or possibly even a direct schematic I can just study. And before anyone says it, I already did LOTS of Googling...

Use a pair of 74181 4-bit ALU chips http://www.datasheetcatalog.org/datasheets/560/493318_DS.pdf

There were Raytheon minicomputers in the late 70's that used to use 4 x 74181 as the heart of the 16-bit CPU using a 25MHz clock speed and a RISC instruction set of 31 instructions.